\((d,1)\)-Total Labelling of Generalized Petersen Graphs \(P(n,k)\)

Abstract

In this paper, we investigate the ( d , 1 ) -total labelling of generalized Petersen graphs P ( n , k ) for d ≥ 3 . We find that the ( d , 1 ) -total number of P ( n , k ) with d ≥ 3 is d + 3 for even n and odd k or even n and k = n 2 , and d + 4 for all other cases.